-
Quaternary Pavonites A1+xSn2−xBi5+xS10 (A+ = Li+, Na+): Site
Occupancy Disorder Defines Electronic StructureJason F. Khoury,†
Shiqiang Hao,‡ Constantinos C. Stoumpos,† Zhenpeng Yao,‡ Christos
D. Malliakas,†
Umut Aydemir,§ Tyler J. Slade,† G. Jeffrey Snyder,‡ Chris
Wolverton,‡ and Mercouri G. Kanatzidis*,†
†Department of Chemistry, Northwestern University, Evanston,
Illinois 60208, United States‡Department of Materials Science and
Engineering, Northwestern University, Evanston, Illinois 60208,
United States§Department of Chemistry, Koc University, Sariyer,
Istanbul 34450, Turkey
*S Supporting Information
ABSTRACT: The field of mineralogy represents an area ofuntapped
potential for the synthetic chemist, as there arenumerous structure
types that can be utilized to formanalogues of mineral structures
with useful optoelectronicproperties. In this work, we describe the
synthesis andcharacterization of two novel quaternary
sulfidesA1+xSn2−xBi5+xS10 (A = Li
+, Na+). Though not natural mineralsthemselves, both compounds
adopt the pavonite structure,which crystallizes in the C2/m space
group and consists of twoconnected, alternating defect rock-salt
slabs of varyingthicknesses to create a three-dimensional lattice.
Despite their commonalities in structure, their crystallography is
noticeablydifferent, as both structures have a heavy degree of site
occupancy disorder that affects the actual positions of the atoms.
Thedifferences in site occupancy alter their electronic structures,
with band gap values of 0.31(2) eV and 0.07(2) eV for the
lithiumand sodium analogues, respectively. LiSn2Bi5S10 exhibits
ultralow thermal conductivity of 0.62 W m
−1 K−1 at 723 K, and thisresult is corroborated by phonon
dispersion calculations. This structure type is a promising host
candidate for futurethermoelectric materials investigation, as
these materials have narrow band gaps and intrinsically low thermal
conductivities.
■ INTRODUCTIONBismuth chalcogenides have garnered widespread
interest, fromsemiconductors and thermoelectrics to
superconductors, owingto their incredible diversity in electronic
structure.1,2 Thelayered narrow gap semiconductors CsBi4Te6 and
RbBi11/3Te6are superconducting at low Tc (4.4 and 3.2 K,
respectively),which is remarkable considering that both compounds
have lowcarrier densities that are not typically conducive to
super-conductive behavior.2,3 Perhaps more importantly, many
newbismuth chalcogenides with relatively complex structures can
bepredictably synthesized from canonical building blocks.
Thediversity and complexity in structure are greatly enhanced
whengroup 14 elements such as Sn2+ and Pb2+ are added.
Thesestructures form several different homologous series
withBi2Te3-, CdI2-, and NaCl-type subunits.
2,4 Further, expressionof the stereoactive lone pair from the
ns2 orbital of Bi3+, Sb3+,Pb2+, and Sn2+ allows for several unique
coordinationenvironments, such as capped octahedra, capped
trigonalprisms, and trigonal bipyramids.3,5 These unusual
perturbationsin local bonding can have broad implications on the
crystal andelectronic structures of extended solids featuring Bi3+,
Sb3+,Pb2+, and Sn2+, resulting in a wide array of novel materials
withemergent properties.6
Many of these materials are known for having considerableamounts
of site occupancy disorder in several naturally
occurring sulfosalts, as long as the other metal can adapt
asimilar coordination environment.7,8 Incredibly, bismuth (andother
similarly sized elements, such as antimony, tin, and lead)can also
have mixed occupancy with alkali metals ofconsiderably smaller
ionic radii so long as they can adapt thesame coordination
environment, as in the case of LiBi3S5
9 andLiPbSb3S6.
10 As a result of these phenomena, there have been aconsiderable
wealth of synthetic sulfosalts and selenosalts thathave significant
site occupancy disorder, the effect of which ontheir electronic
properties has not been thoroughly inves-tigated.11−13
Pavonite (AgBi3S5) is a naturally occurring sulfosalt that
hasshown promise as a thermoelectric material due to its
extremelylow thermal conductivity and good electrical
properties.14
Pavonite is a three-dimensional structure with a layered
rock-salt motif containing two distinct slabs. The first, thicker
PbS-type slab consists of BiS6 octahedra oriented as diagonal
chains,and these chains are flanked by the thinner SnSe-type
slabsconsisting of AgS6 octahedra surrounded by BiS5
squarepyramids.14 The structure pavonite is part of the
homologousseries M′n+1Bi2Qn+5, where the M′ cations can be bismuth,
alkalimetal, lead, silver, or copper, and the Q anions are
sulfur,
Received: December 13, 2017Published: February 7, 2018
Article
pubs.acs.org/ICCite This: Inorg. Chem. 2018, 57, 2260−2268
© 2018 American Chemical Society 2260 DOI:
10.1021/acs.inorgchem.7b03091Inorg. Chem. 2018, 57, 2260−2268
pubs.acs.org/IChttp://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.inorgchem.7b03091http://dx.doi.org/10.1021/acs.inorgchem.7b03091
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selenium, or tellurium.. The original pavonite mineral is the n
=5 member of this homologous series.For AgBi3S5, it has been
proposed that its low thermal
conductivity is the result of a “double rattling” mechanism
withthe phonon modes of the Ag and Bi atoms in the
structure,causing a phonon dampening effect that reduces lattice
thermalconductivity of the material.15 The double rattling
mechanismis where both Ag and Bi atoms have two peaks in the
partialdensity of states as a function of frequency, suggesting
that bothatoms are responsible for suppressing the lattice
thermalconductivity of AgBi3S5. This mechanism is distinct from
theconcerted rattling effect in CsAg5Te3, where the Ag
sublatticeatoms all oscillate in the same phase and only one broad
peakin the partial density of states is observed.16 Rattling
effects inmaterials with complex crystal structures allow for an
additionalmethod of scattering acoustic phonons without
sacrificingperformance in their electrical properties, therefore
makingthem attractive candidates for thermoelectric materials.In
this work, we describe the synthesis, crystal structure, and
characterization of two novel quaternary bismuth
chalcogenidesASn2Bi5S10 (A = Li
+, Na+) with the n = 5 pavonite structure.Although both
compounds have the same structure type, theirdifferences in site
occupancy disorder cause noticeable changesin their electronic
structures and optical properties. Electricalmeasurements on
LiSn2Bi5S10 show that it behaves like a dopedn-type semiconductor
with a conductivity of 165 S/cm andcarrier concentration of 1.21 ×
1019 cm−3 at room temperature.LiSn2Bi5S10 has ultralow thermal
conductivity of 0.625 W m
−1
K−1 at 723 K, which is lower than that of synthetic pavonite
atthe same temperature, likely due to its considerable site
occupancy disorder. Phonon dispersion calculations are used
tocreate simulated lattice thermal conductivity of LiSn2Bi5S10,with
the simulated values being much higher than the actualvalues,
likely due to the significant site occupancy disorder andminor
impurity phase of the experimental compound.
■ EXPERIMENTAL SECTIONReagents. All chemicals in this study were
used as obtained:
bismuth metal (99.9%, Strem Chemicals, Inc., Newburyport,
MA),sulfur pieces (99.998%, Sigma-Aldrich, St. Louis, MO), tin
chunks(99.999%, American Elements, Los Angeles, CA), lithium metal
rods(99.9%, 12.7 mm diameter, Sigma-Aldrich, St. Louis, MO),
andsodium metal (99.95%, Sigma-Aldrich, St. Louis, MO). Li2S and
Na2Swere synthesized from stoichiometric amounts of the
constituentelements reacted in liquid ammonia, as described in the
SupportingInformation.
Synthesis. LiSn2Bi5S10. Li2S (0.2529 g, 5.504 mmol), Sn (1.2594
g,10.609 mmol), Bi (6.6250 g, 31.702 mmol), and S (1.8620 g,
58.079mmol) were loaded in a 13 mm carbon coated silica tube in a
dry,nitrogen glovebox. The tube was flame-sealed under vacuum
atapproximately 2 × 10−3 mbar, heated to 800 °C in 8 h, held there
for 2h, and water quenched to room temperature. This compound was
thensealed in a second 13 mm carbon coated fused silica tube,
heated to800 °C in 24 h, held there for 2 h, and cooled to room
temperature in48 h. The above 1:1:3:6 molar ratio of Li:Sn:Bi:S
with this processresulted in a bulk pure material, but the original
1:2:5:10 ratio hadminor impurities. This excess of lithium accounts
for glass attack withthe tube, and the deficiency of tin is most
likely the result of the bulkmaterial being tin deficient compared
to the ideal stoichiometry. Bulkpure LiSn2Bi5S10 was synthesized by
this process, and crystals suitablefor single crystal diffraction
were obtained by breaking up the ingot.The reaction produced the
product in quantitative yield and is stablein open air at room
temperature.
Table 1. Crystal Data and Structure Refinement for LiSn2Bi5S10
and NaSn2Bi5S10 at 298 K
empirical formula Li0.97(3)Sn2.06(2)Bi4.97(2)S10(0)a
Na1.04(2)Sn1.84(0)Bi5.11(3)S10(0)
b
formula weight 1609.90 1631.95temperature 298 K 298 Kwavelength
0.71073 Å 0.71073 Åcrystal system monoclinic monoclinicspace group
C2/m C2/munit cell dimensions a = 13.148(3) Å, α = 90° a =
13.311(3) Å, α = 90°
b = 4.0186(8) Å, β = 93.93(3)° b = 4.0470(8) Å, β = 93.64(3)°c =
16.607(3) Å, γ = 90° c = 16.794(3) Å, γ = 90°
volume 875.4(3) Å3 902.8(3) Å3
Z 2 2density (calculated) 6.108 g/cm3 6.003 g/cm3
absorption coefficient 53.820 mm−1 53.326 mm−1
F(000) 1356 1376crystal size 0.1745 × 0.1049 × 0.0112 mm3 0.0964
× 0.0531 × 0.0164 mm3
θ range for data collection 2.459 to 29.207° 2.430 to
25.974°index ranges −18 ≤ h ≤ 16, −5 ≤ k ≤ 5, −22 ≤ l ≤ 22 −16 ≤ h
≤ 16, −4 ≤ k ≤ 4, −18 ≤ l ≤ 20reflections collected 4242
3187independent reflections 1349 [Rint = 0.0434] 1008 [Rint =
0.0649]completeness to θ = 26.000°, 25.974° 99.7% 99.9%refinement
method full-matrix least-squares on F2 full-matrix least-squares on
F2
data/restraints/parameters 1349/0/61 1008/0/60goodness-of-fit
1.090 1.279final R indices [I > 2σ(I)] Robs = 0.0390, wRobs =
0.0932 Robs = 0.0675, wRobs = 0.1661R indices [all data] Rall =
0.0490, wRall = 0.0972 Rall = 0.0814, wRall = 0.1710extinction
coefficient 0.00084(11) N/Alargest diff peak and hole 1.717 and
−1.585 e·Å−3 2.945 and −5.082 e·Å−3
aLi0.97(3)Sn2.06(2)Bi4.97(2)S10(0): R = ∑||Fo| − |Fc||/∑|Fo|, wR
= {∑[w(|Fo|2 − |Fc|2)2]/∑[w(|Fo|4)]}1/2 and w = 1/[σ2(Fo2) +
(0.0557P)2 + 4.8554P]where P = (Fo
2 + 2Fc2)/3. bNa1.04(2)Sn1.84(0)Bi5.11(3)S10(0): R =∑||Fo| −
|Fc||/∑|Fo|, wR = {∑[w(|Fo|2 − |Fc|2)2]/∑[w(|Fo|4)]}1/2 and w =
1/[σ2(Fo2) +
(0.0523P)2 + 238.6890P] where P = (Fo2 + 2Fc
2)/3.
Inorganic Chemistry Article
DOI: 10.1021/acs.inorgchem.7b03091Inorg. Chem. 2018, 57,
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NaSn2Bi5S10. Na2S (0.2600 g, 3.331 mmol), Sn (1.4602 g,
12.301mmol), Bi (6.4264 g, 30.751 mmol), and S (1.8735 g, 58.428
mmol)were loaded in a 13 mm carbon coated fused silica tube in a
dry,nitrogen glovebox. Na2S had a 10% molar excess to account for
glassattack with the silica tube. The tube was flame-sealed under
vacuum atapproximately 2 × 10−3 mbar, heated to 800 °C in 8 h, held
there for 2h, and water quenched to room temperature. The reaction
producedthe product in quantitative yield with minor impurities
present in thepowder X-ray diffraction pattern, and is stable in
open air at roomtemperature.Powder X-ray Diffraction. Powder X-ray
diffraction (PXRD)
patterns were taken using a Rigaku Miniflex powder
X-raydiffractometer with Ni-filtered Cu Kα radiation (λ = 1.5406 Å)
witha 30 kV voltage and 15 mA current. The diffraction pattern had
a scanwidth of 0.02° and a scan rate of 10°/min. Simulated PXRD
patternswere created using the software Mercury. Synchrotron
X-raydiffraction was measured on LiSn2Bi5S10 using the
high-resolutiondiffractometer 11BM-B at the Advanced Photon Source
of ArgonneNational Laboratory. The synchrotron sample was measured
at 295 Kwith a nominal 2θ step size of 0.001° and a scan rate of
0.1 step/s. Thewavelength of synchrotron radiation was λ = 0.412642
Å.Single Crystal X-ray Diffraction. An IPDS 2T single crystal
X-ray
diffractometer, running at 50 kV and 40 mA with Mo Kα radiation
(λ= 0.71073 Å), was used to gather data on the crystal structures
ofLiSn2Bi5S10 and NaSn2Bi5S10. Single crystals of both compounds
wereadhered to a glass fiber with super glue, and all data were
collected atroom temperature. The data were collected, analyzed,
and integratedusing the X-AREA17 software, where X-RED integrated
the data andX-SHAPE applied the numerical absorption correction
based on thecrystal’s shape and composition. The data was solved
with SHELXTusing Direct Methods, and refined with SHELXL using the
LeastSquares method.18 The crystallographic information for
bothstructures can be found in Tables 1−3. Additional
crystallographicinformation can be found in the Supporting
Information.
Scanning Electron Microscopy and Energy DispersiveSpectroscopy
(EDS). Images and quantitative analysis (apart fromlithium) were
performed with a Hitachi S-3400 scanning electronmicroscope that
was equipped with a PGT energy-dispersive X-rayanalysis instrument.
Lithium cannot be detected by EDS due to its lowelectron count, so
the results of LiSn2Bi5S10 do not have lithium in theatomic
percentages. To account for this, X-ray photoelectronspectroscopy
(XPS) and inductively coupled plasma optical emissionspectroscopy
(ICP-OES) were used to confirm the presence of lithiumin the
structure. EDS was performed at 25 kV, 70 mA probe current,and a 60
s acquisition time. The chemical compositions of each crystalwere
the result of averaged compositions from multiple single-pointdata
collections.
Differential Thermal Analysis (DTA). Differential
thermalanalysis (DTA) was performed using a Netzsch STA 449 F3
Jupitersimultaneous thermal analysis (STA) instrument. The samples
wereground to a fine powder, loaded into carbon-coated silica
ampules(approximately 40 mg in each ampule), and flame-sealed
undervacuum. Each sample was compared to a sealed silica
ampulecontaining aluminum oxide (Al2O3) of comparable mass. Each
samplewas heated to 800 °C at a rate of 10 °C/min, held at 800 °C
for 5 min,and cooled back down at a rate of 10 °C/min. Each sample
wentthrough two cycles to show that the behavior was repeatable.
AfterDTA was performed, a PXRD of each compound (see
SupportingInformation) was taken to determine if they melted
congruently.
Fourier-Transform Infrared Spectroscopy (FTIR).
Fourier-transform infrared spectroscopy (FTIR) was performed using
aNicolet 6700 IR spectrometer under constant flow of nitrogen with
adiffuse reflectance setup (Figure 4). A metal mirror was used as a
100%reflectance standard that all of the spectra were compared
to.Absorbance (α/S) data were calculated from the FTIR reflectance
datausing the Kubelka−Munk equation (α/S = (1 − R2)/2R), where α
isthe absorption coefficient, S is the scattering coefficient, and
R isreflectance.19 The band gap of the material was estimated by
using alinear fit of the absorption edge.
Density Functional Theory (DFT) Calculations. The totalenergies
and relaxed geometries were calculated by DFT within thegeneralized
gradient approximation (GGA) of Perdew−Burke−Ernzerhof, the
exchange correlation functional with ProjectorAugmented Wave
potentials.20 We use periodic boundary conditionsand a plane wave
basis set as implemented in the Vienna ab initiosimulation
package.21 The total energies were numerically convergedto
approximately 3 meV/cation using a basis set energy cutoff of 500eV
and dense k-meshes corresponding to 4000 k-points per
reciprocalatom in the Brillouin zone.
To do a DFT band structure calculation for a material
withexperimentally determined mixed occupancy of the individual
sites, wefirst identified the lowest energy configuration of
LiSn2Bi5S10 andNaSn2Bi5S10 from many geometrically distinct
Bi/Li(Na)/Snpossibilities. In simpler terms, we enumerate all
structural possibilitieswithin a 72-atom cell and rank their
electrostatic energies. For the 10structures with the lowest
electrostatic energies, we perform furtherDFT calculations to
determine the most favorable (lowest energy)structure. The details
of searching for the most favorable structureshave been applied to
other materials and are described in SupportingInformation.22 After
implementing this strategy, we that found theground state
structures of LiSn2Bi5S10 and NaSn2Bi5S10 are quitedifferent even
though the two materials have the same composition.
Phonon Dispersion Calculations. To quantitatively explore
theorigin of very low lattice thermal conductivity at the atomic
level, weemployed the Debye−Callaway model to quantitatively
evaluate thelattice thermal conductivity of LiSn2Bi5S10. It is
known that theGrüneisen parameters, which characterize the
relationship betweenphonon frequency and crystal volume change,
allow us to estimate thelattice anharmonicity and better understand
the physical nature oflattice thermal conductivity. The phonon and
Grüneisen dispersionsare calculated using first-principles DFT
phonon calculations withinthe quasi-harmonic approximation. The
LiSn2Bi5S10 phonon dis-persions are calculated on a 108 atom cell
at two volumes: one is the
Table 2. Bond Lengths [Å] for LiSn2Bi5S10 at 293(2) K
withEstimated Standard Deviations in Parentheses
label distances
Bi(1)−S(1) 2.582(4)Bi(1)−S(3) 2.774(2)Bi(2)/Li(1)−S(3)
2.642(4)Bi(2)/Li(1)−S(5) 2.745(2)Bi(3)/Sn(1)−S(2)
2.878(3)Bi(3)/Sn(1)−S(4) 2.780(3)Bi(3)/Sn(1)−S(5)
2.665(3)Sn(2)−S(2) 2.825(2)Sn(3)−S(1) 2.825(2)Sn(3)−S(3)
2.479(4)
Table 3. Bond Lengths [Å] for NaSn2Bi5S10 at 293(2) K
withEstimated Standard Deviations in Parentheses
label distances
Bi(1)/Na(1)−S(1) 2.882(7)Bi(1)/Na(1)−S(4)
2.800(8)Bi(1)/Na(1)−S(5) 2.678(11)Bi(2)/Na(2)−S(1)
2.952(10)Bi(2)/Na(2)−S(3) 2.685(10)Bi(2)/Na(2)−S(5)
2.761(7)Bi(3)/Na(3)−S(2) 2.644(11)Bi(3)/Na(3)−S(3)
2.757(7)Sn(1)/Bi(4)−S(2) 2.855(7)Sn(1)/Bi(4)−S(3)
2.733(12)Sn(2)−S(4) 2.914(15)
Inorganic Chemistry Article
DOI: 10.1021/acs.inorgchem.7b03091Inorg. Chem. 2018, 57,
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equilibrium volume V0, and another one is the
isotropicallycompressed volume 0.98V0.The Debye−Callaway
formalism23 has been shown to produce
accurate values of lattice thermal conductivity, compared to
experi-ment, for low-conductivity thermoelectric compounds.24 The
totallattice thermal conductivity can be written as a sum over
onelongitudinal κLA and two transverse κTA and κTA′ acoustic
phononbranches: κLatt = κLA + κTA + κTA′. The partial
conductivities κi (icorresponds to TA, TA′, and LA modes) are given
by
∫∫
∫κ
τ=
−+
ττ
ττ τ
ΘΘ
−
Θ
−
⎧⎨⎪⎪
⎩⎪⎪
⎡⎣⎢
⎤⎦⎥
⎫⎬⎪⎪
⎭⎪⎪
C Tx x
xx
x
13
( ) e(e 1)
dd
di i
T i x
x
T x x
T x x3
0
/c
4
20
/ ( ) e
(e 1)
2
0
/ ( ) e
(e 1)
i
ii x
i x
ii x
i i x
c4
N2
c4
N U2
(1)
In this expression, Θi is the longitudinal (transverse)
Debyetemperature, 1/τN
i is the scattering rate for normal phonon processes,1/τR
i is the sum of all resistive scattering processes, and 1/τci =
1/τN
i +1/τR
i , x = ℏω/kBT, and Ci = kB4/2π2ℏ3vi, here, ℏ is the Planck
constant,
kB is the Boltzmann constant, ω is the phonon frequency, and vi
is thelongitudinal or transverse acoustic phonon velocity.The
resistive scattering rate is the sum of scattering rates due to
Umklapp phonon−phonon scattering (1/τUi ), mass-difference
im-purity scattering (1/τm
i ), boundary scattering (1/τBi ), and electron−
phonon scattering (1/τe−phi ). In the pure single crystal
compounds
considered here, we ignore the effect of impurity scattering,
and weassume that boundary and electron−phonon scattering
contributionscan be ignored at temperatures above approximately 100
K. Thus, theresistive scattering rate is mainly determined by the
Umklappphonon−phonon processes (1/τRi ≅ 1/τUi ). The normal
phononscattering and Umklapp can be written as
τγ
=ℏx
k V
M vx T
1( )N
LAB
5LA
2
4LA
52 5
(2)
τ
γ=
ℏ′′
′x
k V
M vxT
1( )N
TA/TAB
5TA/TA
2
4TA/TA
55
(3)
τγ
=ℏ Θ
θ−
x
k
M vx T
1( )
eii
i i
T
U
B2 2
22 3 /3i
(4)
where γ, V, and M are the Gruneisen parameter, the volume per
atom,and the average mass of an atom in the crystal, respectively.
The
Grüneisen parameter can be defined as γ = − ωω∂∂i
VV
i
i, characterizing the
relationship between phonon frequency and volume
change.Inductively Coupled Plasma Optical Emission Spectroscopy
(ICP-OES). ICP-OES measurements to detect the presence of
lithiumand approximate the molar ratios for LiSn2Bi5S10 were
conductedusing a Thermo iCap 7600 ICP-OES instrument. LiSn2Bi5S10
(5 mg)was dissolved in 0.6 mL of aqua regia, and then diluted to a
10 mLsample with a 3% (by weight) HNO3 solution. All standards and
blanksamples were also diluted with the same 3% HNO3 solution. Due
tothe evolution of H2S gas upon dissolving the compound in aqua
regia,the amount of sulfur was not measured when performing
theexperiment.Spark Plasma Sintering (SPS). Ingots of both
compounds were
ground into fine powders and sieved (53 μm) to ensure small
andhomogeneous particle sizes. These powders were then loaded
into12.7 mm graphite dies, and spark plasma sintering (SPS) with an
SPS-211LX, Fuji Electronic Industrial Co. Ltd., instrument was
performedto turn them into dense ingots suitable for cutting and
polishing forthermoelectric measurements. The sample was placed
under vacuumand 40 MPa of pressure, while the heating profile was
elevated to 500°C in 5 min, held there for another 5 min, and then
cooled to roomtemperature with the sintering turned off. The ingots
created from SPSachieved approximately 93% of the theoretical
density of eachcompound.
Electrical Conductivity and Seebeck Measurements. Elec-trical
conductivity and Seebeck coefficient measurements wereobtained
using an ULVAC Riko ZEM-3 instrument under a low-pressure helium
atmosphere from room temperature to 600 °C. Thesample was cut
perpendicular to SPS pressure with approximatedimensions of 3.5 ×
3.5 × 10 mm3, and were coated with a thin layerof boron nitride on
all sides except the points of electrical contact tominimize
melting during the measurement. The electrical
conductivitymeasurement had an uncertainty of about 10%.25
Hall Effect and Carrier Concentration Measurements.
Roomtemperature Hall coefficient and carrier concentration of
LiSn2Bi5S10were measured on an SPS-obtained pellet (thickness
-
suggest that there is an excess of lithium in the sample, and
thiscan be explained by the presence of a lithium-rich
secondaryphase that can only be detected with synchrotron
X-raydiffraction.The DTA of this compound shows a dominant melting
event
at 677 °C and a shoulder melting event at approximately 690°C,
with matching crystallization events at 661 and 677 °C. Thedominant
melting event and its shoulder correspond to theprimary phase
LiSn2Bi5S10 and the secondary n = 4 pavonitephase, respectively.
The fact that the melting points of the twophases are so close
together further suggests that they are in thesame homology, as
different n-members of homologous seriestend to have incremental
changes in their physical properties.6
NaSn2Bi5S10 was synthesized at the nominal 1:2:5:10 molarratio
of Na:Sn:Bi:S, and the PXRD showed the presence of theintended
major pavonite phase along with a minor secondaryphase
Sn0.22Bi1.78S2.88.
27 The DTA showed melting events at673 and 625 °C for the major
and minor phases, respectively,with crystallization events at
approximately the same temper-atures for each. The compound could
not be sintered into apellet for thermoelectric measurements, as
the structuredecomposes when it is annealed. This indicates
thatNaSn2Bi5S10 is a kinetic phase that is only isolable
viaquenching from the melt, whereas LiSn2Bi5S10 is a morerobust,
thermodynamic phase.
Structure Description. LiSn2Bi5S10 and NaSn2Bi5S10
weredetermined to have the pavonite structure type, which
consistsof two alternating rock-salt (either PbS- or SnSe-type)
slabsthat were cut perpendicular to the [311] direction of the
cubicrock-salt lattice. (See Figure 3.) The three-dimensional
structure is anisotropic and part of the homologous
seriesM′n+1Bi2Qn+5, where the M′ cations can be bismuth,
alkalimetal, lead, silver, or copper, and the Q anions are sulfur
or
Figure 1. Powder X-ray diffraction patterns (Cu Kα radiation, λ
=1.5406 Å) and differential thermal analysis (DTA) graphs
ofLiSn2Bi5S10 (A and C, respectively) and NaSn2Bi5S10 (B and
D,respectively). There is a shoulder melting event in B at 693 °C,
but nosecondary phase in the PXRD pattern, suggesting the presence
of ahigh temperature precipitate redissovled into the matrix.
Themetastable phase NaSn2Bi5S10 also has a minor secondary phase
thatmelts at 625 °C.
Figure 2. Synchrotron X-ray diffraction (SXRD, λ = 0.412642 Å)
andLeBail fit of LiSn2Bi5S10. The fit suggests that the
lithium-richsecondary phase is an n = 4 pavonite, as the lattice
parameters of thesecondary phase are a = 13.1933(2) Å, b =
4.02963(6) Å, c =15.0152(2) Å, β = 99.233(1)°.
Figure 3. Crystal structures of LiSn2Bi5S10 (left) and
NaSn2Bi5S10 (right). Both contain the same motif of pseudolayered
alternating rock-salt slabs,but the right structure is notable in
how the alkali metal is distributed across the bismuth sites.
Figure 4. FTIR diffuse reflectance data for LiSn2Bi5S10 (left)
andNaSn2Bi5S10 (right), with measured band gaps of 0.31(2) and
0.07(2)eV, respectively.
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selenium. The naturally occurring pavonite mineral,
AgBi3S5,along with the two compounds described in this work, are
the n= 5 member of this homologous series. In this structure
type,the thinner slab (Slab I) is invariant to changes in the
n-member and consists of [M′S6] octahedra flanked by two[BiS5]
square pyramids, forming SnSe-type layers along the[010] direction.
The thicker slab (Slab II) is a distorted PbS-type structure
fragment, incorporated in pavonite along the[111] direction. The
number of face-sharing octahedra in adiagonal chain is equal to the
number of the n-member.28
For LiSn2Bi5S10, Slab I is unique in that the M′ in the
M′S6octahedron is a site of mixed occupancy, where it is a
[LiS6]octahedron in 72% of unit cells and a [SnS6] octahedron in
theother 28%, and the surrounding coordination environments arethe
same [BiS5] square pyramids that are common for thisstructure.
While it is remarkable that ions of such differing sizesas Li+ and
Sn2+ (0.76 and 1.18 Å, respectively) can occupy thesame site, there
is precedence for this phenomenon in otherdisordered pavonite
structures containing lithium.9 The shorterbond lengths are also
evidence of mixed occupancy, as theunique bonds at the mixed site
(2.479(4) Å and 2.825(2) Å)are on average shorter than that of the
unmixed [SnS6] site(2.825(2) Å and 2.888(4) Å) in the structure.
The largeasymmetry of the [(Li/Sn)S6] site suggests that it is a
veryaxially distorted octahedron (where both axial bonds
are2.479(4) Å) that has four weaker equatorial bonds of 2.825(2)Å
in length. [(Li/Sn)S6] is similar to the AgS6 octahedron
insynthetic pavonite, where they are both axially distorted.
Theaxial and equatorial bonds for the AgS6 octahedron are2.741(6) Å
and 2.917(2) Å, respectively.7 Slab II is slightlymore complicated
in terms of mixed occupancy, as the fiveoctahedra along the
one-dimensional chain are either [SnS6],[(Bi/Li)S6], or
[(Bi/Sn)S6]. The Bi/Li site is split 87% to 13%in terms of
occupancy, and the Bi/Sn site is split 61% to 39%.The unique bonds
at the Bi/Li site (2.745(3) Å and 2.642(4)Å) are slightly shorter
than the Bi/Sn site (2.780(3) Å and2.665(3) Å), which is
unsurprising considering that the formercontains the significantly
smaller lithium cation and the latter ismixed with two atoms of
almost identical ionic radii. Thesebond lengths are comparable to
established literature bondlengths for bismuth sulfide and tin
sulfide, with the former
ranging from 2.697(14) Å to 2.961(11) Å and the latter
rangingfrom 2.622(3) Å to 2.6618(19) Å.NaSn2Bi5S10 is also an n = 5
pavonite, but there are several
notable differences in the occupancies of the metal sites in
bothSlab I and Slab II of the structure. The [M′S6] octahedron
inSlab I is actually a Sn/Bi site (84% and 16% respectively)
anddoes not contain any monovalent alkali metals. [(Sn/Bi)S6]
isalso a distorted octahedron, but not to the same extent as
thelithium analogue, as the axial bonds are 2.734(12) Å and
theweaker equatorial bonds are 2.856(7) Å. The
[(Sn/Bi)S6]octahedron is surrounded by two [(Bi/Na)S5] square
pyramids,where the occupancies are 79% and 21% respectively. In
Slab II,the different octahedra along the diagonal chains are
either[SnS6] or two unique [(Na/Bi)S6] octahedra. The Sn−S
bondlengths are comparable to similar bonds in the lithium
pavonitestructure with values of 2.866(7) Å and 2.917(15) Å, and
thevalues of the Na/Bi bonds across all three sites range
from2.644(10) Å to 2.950(10) Å in length. In both structures,
thebismuth- and tin-containing octahedra are distorted due to
theirstereoactive lone pairs (6s2 for and 5s2 for bismuth and
tin,respectively), which persists despite the presence of
mixedoccupancy with alkali metals at the sites.29
Optical Measurements and Electronic StructureCalculations. Both
LiSn2Bi5S10 and NaSn2Bi5S10 are directband gap semiconductors with
values of 0.31(2) eV and0.07(2) eV respectively. The fact that the
band gap of thesodium analogue is significantly smaller occurs due
todifferences in mixed occupancy of the individual sites. Insteadof
sodium being primarily localized to the pseudo-octahedralgeometry
of Slab I in the structure, it is spread out relativelyevenly
across the bismuth sites in Slab II, significantly alteringthe band
structure of the material relative to its analogue. Thedifferences
in site occupancy disorder for the two structures arecorroborated
by the band structures of both compounds, asDFT predicts a wider
band gap for the lithium pavonitestructure compared to its sodium
counterpart (Figure 5).The band structures for LiSn2Bi5S10 and
NaSn2Bi5S10 are
significantly different, as seen in Figure 5. The predicted
bandgap for LiSn2Bi5S10 (0.25 eV) is in good agreement with thetrue
band gap of 0.31(2) eV, but the predicted gap of thesodium analogue
(0.15 eV) is actually higher than the true gapthat is measured
experimentally (0.07(2) eV), an anomalous
Figure 5. (A, B) Electronic band structures for LiSn2Bi5S10 and
NaSn2Bi5S10 respectively. The Fermi level is at 0 eV in both
graphs. (C, D) Partialand full density of states for LiSn2Bi5S10
and NaSn2Bi5S10 respectively. The alkali metal is not included due
to minimal contribution to either theVBM or CBM of each
structure.
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result given the tendency of DFT to underestimate band gaps.The
densities of states (DOS) for each structure were similar inthat
the valence band maximum (VBM) of both compounds iscomposed of Sn
5s and S 3p character, and the conductionband minimum (CBM) is
almost entirely Bi 6p character withminimal contribution from Sn 5s
orbitals. The alkali metal inboth cases has a negligible effect on
the density of states, astheir highest occupied orbitals are not
close enough in energyto contribute to the band edges. However,
even though thealkali metals do not directly contribute to the
density of states,their presence in each structure is important due
to thedifferences in site occupancy disorder. Their differing ionic
radiidictate which atoms they share occupancy with, and this in
turnalters the individual DOS peaks for each atom listed,
resultingin the vastly different band structures presented in
Figure 5.The valence bands differ in that LiSn2Bi5S10 has much
broaderbands, but NaSn2Bi5S10 has much more dispersive bands.
Theopposite is true in the conduction bands of the two
structures,as the conduction band is much more dispersive in
LiSn2Bi5S10and broader in the sodium analogue.Electrical and
Thermal Measurements. Thermoelectric
measurements were performed on LiSn2Bi5S10 to determine
itspotential for this application (see Figure 6).
Thermoelectric
materials and their efficiency are governed by the equation
= σκ
ZT S T2
, where ZT is the dimensionless figure of merit, σ is
the electrical conductivity, S is the Seebeck coefficient, T
isabsolute temperature, and κ is the total thermal
conductivity(which has both lattice and electronic components).
Mostattempts to improve ZT values in thermoelectric materials
havecome from optimization of known, high symmetry materialsthrough
various methods such as doping,30,31 nanostructur-ing,32,33 and
band convergence.34,35 One other paradigm forpursuing high ZT
thermoelectrics is the investigation ofmaterials with complex
crystal and electronic structures aswell as large unit cells, such
as ternary and quaternarychalcogenides with ultralow thermal
conductivity.36,37 Bismuthchalcogenides comprise a significant
portion of all thermo-electric research, as Bi2−xSbxTe3 remains the
prototypical
example of a material that can be utilized near roomtemperature
for practical applications.38
LiSn2Bi5S10 behaves as a doped n-type semiconductor with
aconductivity of around 165 S/cm at room temperature. Itdecreases
with metal-like behavior until around 700 K, wherethe conductivity
stops falling and then slightly increases due tobipolar diffusion.
Hall effect measurements show a carrierconcentration of
approximately 1.2 × 1019 cm−3, while theSeebeck coefficient starts
at −55 μV/K, increases in magnitudeto −160 μV/K, and undergoes a
similar turnover at 700 K tothe electrical conductivity, consistent
with an increase in carrierconcentration as a result of bipolar
diffusion.LiSn2Bi5S10 has very low thermal conductivity (i.e.,
below 1
W m−1 K−1) of 0.80 W m−1 K−1 at room temperature. Thethermal
conductivity decreases to a minimum of 0.625 W m−1
K−1 at 723 K, highlighting the intrinsically low
thermalconductivity of this structure. The pavonite structure
hasbeen previously reported to have ultralow thermal
conductivityfor several different compounds due to its lower
symmetry,complex crystal structure, and the presence of heavy
elementssuch as bismuth.14,26 However, the thermal conductivity of
theLiSn2Bi5S10 is comparable to that of synthetic pavonite(AgBi3S5)
at room temperature (0.75 W m
−1 K−1) and lowerat high temperatures, which is most likely
attributable to theconsiderable site occupancy disorder and more
complexcomposition of its structure compared to the original
mineral.14
The theoretically simulated lattice thermal conductivity,using
an ordered supercell of LiSn2Bi5S10, is significantly higherthan
the actual experimental result. The higher lattice
thermalconductivity is attributable to the quantitative limitations
ofDFT to accurately depict the amount of phonon scattering in
astructure with as much disorder as LiSn2Bi5S10. The highervalue is
also attributable to the fact that the experimentalsample has a
minor secondary phase of n = 4 pavonite, possiblyhelping to scatter
phonons and lowering the experimentalthermal conductivity. However,
the qualitative trends are ingood agreement, as the lattice thermal
conductivities bothdecrease monotonically as a function of
temperature in boththe experimental and simulated cases. The
lattice thermalconductivity in bismuth sulfide at room temperature
isapproximately 1.3 W m−1 K−1, which is almost double that
ofLiSn2Bi5S10 at the same temperature (0.743 W m
−1 K−1),supporting the claim that the lower symmetry and
siteoccupancy disorder of the pavonite structure play a role in
itsultralow thermal conductivity.39 In addition, the
distortiveenvironment of the Sn and Bi atoms from the stereoactive
lone-pair s2 electrons and their pronounced repulsive
interactionsmay also play a role in lowering the thermal
conductivity ofLiSn2Bi5S10.
40
The calculated phonon dispersion of LiSn2Bi5S10 shows thatthe
transverse acoustic phonon modes have slower velocities(and thus
lower thermal conductivity along that path) than thelongitudinal
mode along all three axes (Figure 7). In theBrillouin zone, Γ to Z
corresponds to the a direction, Γ to Xcorresponds to the b
direction, and Γ to Y corresponds to the cdirection. The transverse
modes are similar in the c direction(through the layers), different
in the a direction (between thelayers), and comparably spaced in
the b direction (stackingboth slabs), with the red transverse mode
being consistentlylower in every direction. The Brillouin zone
highlights theanisotropy of the pavonite structure type, as phonon
transportis significantly different depending on the crystal
direction. Thephonon density of states shows that acoustic phonon
transport
Figure 6. Thermoelectric property measurements for
LiSn2Bi5S10.Electrical conductivity (A), Seebeck coefficient (B),
total thermalconductivity (C), and experimental and simulated
lattice thermalconductivity (D).
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in this material is primarily based on the motions of the
heavierbismuth atoms with minimal contribution from tin. Thephonon
dispersion calculations are consistent with theintrinsically low
thermal conductivity of the structure as wellas its anisotropic
nature.
■ CONCLUSIONSThe crystal structures of LiSn2Bi5S10 and
NaSn2Bi5S10 displayconsiderable site occupancy disorder of the
alkali metal on bothBi and Sn sites, and their differences in site
occupancy disordersignificantly alter their band structures and
their opticalproperties. The thermal conductivity of LiSn2Bi5S10 is
ultralowdue to the intrinsic attributes of the pavonite structure
as wellas its complex composition and site occupancy
disorder.Phonon dispersion calculations highlight the anisotropic
natureof the structure, as the transverse acoustic phonon modes
donot facilitate phonon transport as easily as the
longitudinalacoustic phonon mode. The lattice contribution to
thermalconductivity should increase as the n-member in
thehomologous series increases, as the structure would becomemore
and more isotropic and the symmetry of the structurewould trend
toward a defect rock-salt such as Bi2S3. Thepavonite structure is a
promising host candidate for thermo-electric investigation, as
these materials inherently have lowthermal conductivity and narrow
band gaps. There is also aconsiderable phase space to explore, as
the respectivehomologous series could lead to high performing
thermo-electric materials as well as materials with tunable
electronicproperties.
■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting
Information is available free of charge on theACS Publications
website at DOI: 10.1021/acs.inorg-chem.7b03091.
Additional experimental details, crystallographic tables,PXRDs,
SEM-EDS, ICP-OES, and thermoelectricproperty measurements (PDF)
Accession CodesCCDC 1811757−1811758 contain the supplementary
crystal-lographic data for this paper. These data can be obtained
free ofcharge via www.ccdc.cam.ac.uk/data_request/cif, or by
email-ing [email protected], or by contacting
TheCambridge Crystallographic Data Centre, 12 Union Road,Cambridge
CB2 1EZ, UK; fax: +44 1223 336033.
■ AUTHOR INFORMATIONCorresponding Author*E-mail:
[email protected] F. Khoury:
0000-0003-4769-6730Constantinos C. Stoumpos:
0000-0001-8396-9578Chris Wolverton: 0000-0003-2248-474XMercouri G.
Kanatzidis: 0000-0003-2037-4168NotesThe authors declare no
competing financial interest.
■ ACKNOWLEDGMENTSThis work was supported by the National Science
FoundationGrant DMR-1708254, as well as the NASA Science
MissionDirectorate’s Radioisotope Power Systems
ThermoelectricTechnology Development. S.H. and C.W. (DFT
calculations)were supported by the Department of Energy, Office of
ScienceBasic Energy Sciences Grant DE-SC0014520. C.D.M.
wassupported by IMSERC at Northwestern University, which
hasreceived support from the Soft and Hybrid
NanotechnologyExperimental (SHyNE) Resource (NSF NNCI-1542205);
theState of Illinois; and International Institute for
Nanotechnology(IIN). We acknowledge the use of QUEST, the
supercomputerresource facility at Northwestern University. We thank
MichaelL. Aubrey for helpful discussions, and Daniel G. Chica
forassisting in ammonia synthesis of Na2S and Li2S.
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